A body mass m is attached to the lower end of a spring whose upper end is fixed. The spring has neglible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3s. When the mass m is increased by 1 kg, the time period of oscillations becomes 5s. The value of m in kg is-
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When two displacements represented by y1=asin(ωt) and y2=bcos(ωt) are superimposed,the motion is -
(1) not a simple harmonic
(2) simple harmonic with amplitude a/b
(3) simple harmonic with amplitude
(4) simple harmonic with amplitude (a+b)/2
A partricle is executing a simple harmonic motion. Its maximum acceleration is α and maximum velocity is β. Then, its time period of vibration will be
(1)β2/α2
(2)α/β
(3)β2/α
(4)2πβ/α
The damping force on an oscillator is directly proportional to the velocity.The units of the constant of proportionality are
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1. | simple harmonic motion of frequency \(\frac{\omega}{\pi}\). |
2. | simple harmonic motion of frequency \(\frac{3\omega}{2\pi}\). |
3. | non-simple harmonic motion. |
4. | simple harmonic motion of frequency \(\frac{\omega}{2\pi}\). |
The period of oscillation of a mass \(M\) suspended from a spring of negligible mass is \(T.\) If along with it another mass \(M\) is also suspended, the period of oscillation will now be:
1. \(T\)
2. \(T/\sqrt{2}\)
3. \(2T\)
4. \(\sqrt{2} T\)
Two simple harmonic motions of angular frequency \(100~\text{rad s}^{-1}\) and \(1000~\text{rad s}^{-1}\) have the same displacement amplitude. The ratio of their maximum acceleration will be:
1. \(1:10\)
2. \(1:10^{2}\)
3. \(1:10^{3}\)
4. \(1:10^{4}\)
A point performs simple harmonic oscillation of period T and the equation of motion is given by x= a sin .After the elapse of what fraction of the time period the velocity of the point will be equal to half to its maximum velocity?
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